A hovercraft takes off from a platform. Its height (in meters), $x$ seconds after takeoff, is modeled by: $h(x)=-3(x-3)^2+108$ How many seconds after takeoff will the hovercraft land on the ground?
The hovercraft lands on the ground when $h(x)=0$. $\begin{aligned} h(x)&=0 \\\\ -3(x-3)^2+108&=0 \\\\ -3(x-3)^2&=-108 \\\\ (x-3)^2&=36 \\\\ \sqrt{(x-3)^2}&=\sqrt{36} \\\\ x-3&=\pm6 \\\\ x&=\pm6+3 \\\\ x=9&\text{ or }x=-3 \end{aligned}$ We found that $h(x)=0$ for $x=9$ or $x=-3$. Since $x=-3$ doesn't make sense in our context, the only reasonable answer is $x=9$. In conclusion, the hovercraft will land on the ground after $9$ seconds.